GALOIS-THEORETIC CHARACTERIZATION OF ISOMORPHISM CLASSES OF MONODROMICALLY FULL HYPERBOLIC CURVES OF GENUS ZERO

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Abstract

Let l be a prime number. In the present paper, we prove that the isomorphism class of an l-monodromically full hy-perbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-l outer Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a result due to S. Mochizuki which asserts that the isomorphism class of an elliptic curve which does not admit complex multiplication over a number field is completely determined by the kernels of the natural Galois representations on the various finite quotients of its Tate module.

Journal

  • Nagoya Mathematical Journal

    Nagoya Mathematical Journal (203), 47-100, 2011

    Duke University Press

Codes

  • NII Article ID (NAID)
    120003477796
  • NII NACSIS-CAT ID (NCID)
    AA00750899
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0027-7630
  • Data Source
    IR 
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